COMPASSES, PROPORTIONAL, are those whose joint lies between the points terminating each leg: Plate they are either simple or compound. In the former sort CCCXIII. the centre is fixed, so that one pair of these serves only for one proportion.
Compound proportional COMPASSES consist of two branches, each pointed at either end with steel: the length of the branches is cut through, for a cursor to slide up and down; in the middle of which cursor is a
Compasses. screw, serving to join the branches, and to fix them at any point required. On the one leg are divisions, serving to divide lines into any number of equal parts, for reducing of figures, &c. On the other are numbers, for inscribing any regular polygon in a circle proposed.
The use of the first is easy. Suppose, v. gr. a right line required to be divided into three equal parts; push the cursor till the screw be just on the figure 3; where fixing it, take the length of the given line between the longest part of the legs: the distance between the two shortest will be one-third of the given line. In the same manner may the line be divided into any other number of parts.
For the use of the line of polygons. Suppose, v. gr. a pentagon required to be inscribed in a circle; push the cursor till the middle of the screw be against 5, the number of sides in a pentagon; between the shortest parts of the legs take the diameter of the circle: the legs thus opened, the distance between the points of the longest parts will be the side of the pentagon to be inscribed in the circle. And thus for a figure of any other number of sides.